# 用于计算python中的体积或表面积的良好算法

``````import numpy as np
from tvtk.api import tvtk

def main():
# Generate some data with anisotropic cells...
# x,y,and z will range from -2 to 2, but with a
# different (20, 15, and 5 for x, y, and z) number of steps
x,y,z = np.mgrid[-2:2:20j, -2:2:15j, -2:2:5j]
r = np.sqrt(x**2 + y**2 + z**2)

dx, dy, dz = [np.diff(it, axis=a)[0,0,0] for it, a in zip((x,y,z),(0,1,2))]

# Your actual data is a binary (logical) array
data = (r <= max_radius).astype(np.int8)

ideal_volume = 4.0 / 3 * max_radius**3 * np.pi
coarse_volume = data.sum() * dx * dy * dz
est_volume = vtk_volume(data, (dx, dy, dz), (x.min(), y.min(), z.min()))

coarse_error = 100 * (coarse_volume - ideal_volume) / ideal_volume
vtk_error = 100 * (est_volume - ideal_volume) / ideal_volume

print 'Ideal volume', ideal_volume
print 'Coarse approximation', coarse_volume, 'Error', coarse_error, '%'
print 'VTK approximation', est_volume, 'Error', vtk_error, '%'

def vtk_volume(data, spacing=(1,1,1), origin=(0,0,0)):
data[data == 0] = -1
grid = tvtk.ImageData(spacing=spacing, origin=origin)
grid.point_data.scalars = data.T.ravel() # It wants fortran order???
grid.point_data.scalars.name = 'scalars'
grid.dimensions = data.shape

iso = tvtk.ImageMarchingCubes(input=grid)
mass = tvtk.MassProperties(input=iso.output)
return mass.volume

main()
``````

``````Ideal volume 14.1371669412
Coarse approximation 14.7969924812 Error 4.66731094565 %
VTK approximation 14.1954890878 Error 0.412544796894 %
``````
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